Calculative technique to correct for the change in linear accelerator beam energy at off-axis points

Dose uncertainties in photon pencil kernel calculations at off-axis positions

The purpose of this study was to investigate the specific problems associated with photon dose calculations in points located at a distance from the central beam axis. These problems are related to laterally inhomogeneous energy fluence distributions and spectral variations causing a lateral shift in the beam quality, commonly referred to as off-axis softening (OAS). We have examined how the dose calculation accuracy is affected when enabling and disabling explicit modeling of these two effects. The calculations were performed using a pencil kernel dose calculation algorithm that facilitates modeling of OAS through laterally varying kernel properties. Together with a multi-source model that provides the lateral energy fluence distribution this generates the total dose output, i.e., the dose per monitor unit, at an arbitrary point of interest. The dose calculation accuracy was evaluated through comparisons with 264 measured output factors acquired at 5, 10, and 20 cm depth in four different megavoltage photon beams. The measurements were performed up to 18 cm from the central beam axis, inside square fields of varying size and position. The results show that calculations including explicit modeling of OAS were considerably more accurate, up to 4%, than those ignoring the lateral beam quality shift. The deviations caused by simplified head scatter modeling were smaller, but near the field edges additional errors close to 1% occurred. When enabling full physics modeling in the dose calculations the deviations display a mean value of -0.1%, a standard deviation of 0.7%, and a maximum deviation of -2.2%. Finally, the results were analyzed in order to quantify and model the inherent uncertainties that are present when leaving the central beam axis. The off-axis uncertainty component showed to increase with both off-axis distance and depth, reaching 1% (1 standard deviation) at 20 cm depth.

Modelling lateral beam quality variations in pencil kernel based photon dose calculations

Standard treatment machines for external radiotherapy are designed to yield flat dose distributions at a representative treatment depth. The common method to reach this goal is to use a flattening filter to decrease the fluence in the centre of the beam. A side effect of this filtering is that the average energy of the beam is generally lower at a distance from the central axis, a phenomenon commonly referred to as off-axis softening. The off-axis softening results in a relative change in beam quality that is almost independent of machine brand and model. Central axis dose calculations using pencil beam kernels show no drastic loss in accuracy when the off-axis beam quality variations are neglected. However, for dose calculated at off-axis positions the effect should be considered, otherwise errors of several per cent can be introduced. This work proposes a method to explicitly include the effect of off-axis softening in pencil kernel based photon dose calculations for arbitrary positions in a radiation field. Variations of pencil kernel values are modelled through a generic relation between half value layer (HVL) thickness and off-axis position for standard treatment machines. The pencil kernel integration for dose calculation is performed through sampling of energy fluence and beam quality in sectors of concentric circles around the calculation point. The method is fully based on generic data and therefore does not require any specific measurements for characterization of the off-axis softening effect, provided that the machine performance is in agreement with the assumed HVL variations. The model is verified versus profile measurements at different depths and through a model self-consistency check, using the dose calculation model to estimate HVL values at off-axis positions. A comparison between calculated and measured profiles at different depths showed a maximum relative error of 4% without explicit modelling of off-axis softening. The maximum relative error was reduced to 1% when the off-axis softening was accounted for in the calculations.

Sensitivity of megavoltage photon beam Monte Carlo simulations to electron beam and other parameters

The BEAM code is used to simulate nine photon beams from three major manufacturers of medical linear accelerators (Varian, Elekta, and Siemens), to derive and evaluate estimates for the parameters of the electron beam incident on the target, and to study the effects of some mechanical parameters like target width, primary collimator opening, flattening filter material and density. The mean energy and the FWHM of the incident electron beam intensity distributions (assumed Gaussian and cylindrically symmetric) are derived by matching calculated percentage depth-dose curves past the depth of maximum dose (within 1% of maximum dose) and off-axis factors (within 2sigma at 1% statistics or less) with measured data from the AAPM RTC TG-46 compilation. The off-axis factors are found to be very sensitive to the mean energy of the electron beam, the FWHM of its intensity distribution, its angle of incidence, the dimensions of the upper opening of the primary collimator, the material of the flattening filter and its density. The off-axis factors are relatively insensitive to the FWHM of the electron beam energy distribution, its divergence and the lateral dimensions of the target. The depth-dose curves are sensitive to the electron beam energy, and to its energy distribution, but they show no sensitivity to the FWHM of the electron beam intensity distribution. The electron beam incident energy can be estimated within 0.2 MeV when matching either the measured off-axis factors or the central-axis depth-dose curves when the calculated uncertainties are about 0.7% at the 1 sigma level. The derived FWHM (+/-0.1 mm) of the electron beam intensity distributions all fall within 1 mm of the manufacturer specifications except in one case where the difference is 1.2 mm.

Measured water transmission curves and calculated zero field size tumor maximum ratios for 4, 6, and 15 MV x-rays

A multihole diverging Cerrobend plug for megavoltage energies was used to measure water transmission values at different locations in a 20 x 20 cm field at 100 cm source-to-axis distance (SAD) for 4, 6, and 15 MV therapy photon beams. The transmission curves in water were measured at 25 locations across the 20 x 20 field, and each location was separated by 5 cm at the isocenter. Each transmission value was made using a 0.3175 cm diameter (0.079 cm2 area) hole of 20 cm length at the central axis (CAX). The small field measured transmission curve in water was used to derive the zero field size tumor maximum ratio (TMR) and the primary photon exposure spectrum as a function of energy at depth. The exposure spectrum was used to find an effective photon energy and linear attenuation coefficient at depth and at different locations in the field. These values were found to vary with location in the field.

Photon beam quality specification by narrow-beam transmission measurements

Radiation quality specifications in megavoltage photon beams are usually based on depth-dose measurements performed under reference conditions. Stopping-power ratios and various correction factors are then related to parameters such as TPR(10)20, which are extracted from depth-dose measurements. Stopping-power ratio determinations based on this concept were shown to be in error by more than 2% at high energies. Furthermore, electrons generated in the treatment head can, at high energies, contribute to the dose at a depth of 10 cm and thus significantly affect the TPR(10)20 ratio. This method was further shown to be inadequate when the dose in other parts of the field than the reference point was to be measured with ionization chamber dosimetry. A new standardized device for determining photon beam quality based on half value layer (HVL) measurements in water was developed and thoroughly investigated in both a low-energy, (4 MV) and a high-energy beam. A relation between HVL and stopping-power ratios water-to-air was determined by comparative measurements with air ionization chambers and liquid-filled ionization chambers together with Fricke dosimetry. Furthermore, different radiation quality gradients in the photon fields for different types of field-flattening systems, and field-compensating methods were discussed.

Calibration of a portal imaging device for high-precision dosimetry: a Monte Carlo study

Today electronic portal imaging devices (EPID's) are used primarily to verify patient positioning. They have, however, also the potential as 2D-dosimeters and could be used as such for transit dosimetry or dose reconstruction. It has been proven that such devices, especially liquid filled ionization chambers, have a stable dose response relationship which can be described in terms of the physical properties of the EPID and the pulsed linac radiation. For absolute dosimetry however, an accurate method of calibration to an absolute dose is needed. In this work, we concentrate on calibration against dose in a homogeneous water phantom. Using a Monte Carlo model of the detector we calculated dose spread kernels in units of absolute dose per incident energy fluence and compared them to calculated dose spread kernels in water at different depths. The energy of the incident pencil beams varied between 0.5 and 18 MeV. At the depth of dose maximum in water for a 6 MV beam (1.5 cm) and for a 18 MV beam (3.0 cm) we observed large absolute differences between water and detector dose above an incident energy of 4 MeV but only small relative differences in the most frequent energy range of the beam energy spectra. It is shown that for a 6 MV beam the absolute reference dose measured at 1.5 cm water depth differs from the absolute detector dose by 3.8%. At depth 1.2 cm in water, however, the relative dose differences are almost constant between 2 and 6 MeV. The effects of changes in the energy spectrum of the beam on the dose responses in water and in the detector are also investigated. We show that differences larger than 2% can occur for different beam qualities of the incident photon beam behind water slabs of different thicknesses. It is therefore concluded that for high-precision dosimetry such effects have to be taken into account. Nevertheless, the precise information about the dose response of the detector provided in this Monte Carlo study forms the basis of extracting directly the basic radiometric quantities photon fluence and photon energy fluence from the detector's signal using a deconvolution algorithm. The results are therefore promising for future application in absolute transit dosimetry and absolute dose reconstruction.

A generic off-axis energy correction for linac photon beam dosimetry

Cooperative clinical trial group protocols frequently require off-axis point dose calculations. The Radiological Physics Center uses the calculative technique developed by Hanson et al. [Med. Phys. 7, 145-146 (1980); 7, 147-150 (1980)] to verify these calculations. In order to correct for off-axis energy changes, this technique requires off-axis half-value layer data, HVL, as a function of off-axis ray angle for the specific beam. This paper presents a formulism based on HVL mesurements on a limited number of therapy beams, which allows the calculation of an off-axis energy-correction factor for any clinical photon beam created by a linear accelerator using conventional flattening filters.

Linear accelerator photon beam quality at off-axis points

Transmitted intensity through water was measured in a narrow-beam geometry for different energy x-ray beams from commercial accelerators. In order to accurately obtain the attenuation coefficient of the incident beam using transmission data, a novel formula was developed based on consideration of beam hardening in phantom. The value of the attenuation coefficient obtained by fitting transmission data to this formula was found to be independent of the absorber thickness used in experiments, whereas the attenuation coefficient obtained from the traditional formula, I(x) = I0 exp(-mux), changed by up to 7% with absorber thickness for a given beam. The beam hardening coefficient obtained from our formula indicates that the attenuation coefficient in water changes by about 0.33% per cm near the surface for the high-energy photon beams studied. Variations in beam quality with off-axis distance were subsequently investigated using the new formula. Results show that the attenuation coefficient at the water surface increased by about 15% for 15 and 18 MV beams, and by 11%-13% for 6 MV beams, when the off-axis distance at 100 cm from the source was changed from 0 to 18 cm. Consideration of the physics of bremsstrahlung production suggests that these variations should be mainly determined by the shape of the flattening filter, i.e., by the path length of rays traversing the filter in different directions. This expectation was confirmed by observing that the attenuation coefficient at the phantom surface can be related to the ray path of the beam in the flattening filter using the new transmission formula.

10 MV x-ray zero-area phantom scatter correction factors (Sp) obtained using three extrapolation methods

Three sets of 10 MV x-ray zero-area phantom scatter correction factors (Sp) have been obtained using three methods. The three methods are all based on the Bjärngard-Petti extrapolation principle. The three sets of data assume lateral CPE (charged particle equilibrium) for the primary absorbed dose. Using the most reliable set of data, a set of 10 MV x-ray SMRs (scatter-maximum ratios) is produced and parameterized. With respect to the zero-area Sp correction factor at a depth of 2.5 cm, the parameterized expression gives Sp (0; 2.5) = 0.931 and a Rice-Chin Monte Carlo simulation gives Sp (0; 2.5) = 0.927. The former is only 0.4% larger than the latter.

Dosimetry of the Siemens Mevatron 67 linear accelerator

Measurements have been made on a Siemens Mevatron 67 linear accelerator. The change of beam quality has been measured as a function of position off-axis and compared to another Siemens 6 MV linear accelerator. Similarly, beam profiles are compared to a Siemens Mevatron VI. Additional measurements include entrance dose, inverse square applicability, central axis percent depth dose, tissue-maximum ratios, output factors, wedge factors and block transmission factors. Comparison is made with an Atomic Energy of Canada Limited Therac 6 and Varian Clinac 6-100.